Let V, W E R3 be non-zero orthogonal vectors and let T: R3 - R3 be the linear transfor- mation defined by T( x) = 2 projy (x) + 2 projw( x) - and let A = [The be its standard matrix. (a) Prove that A2 = 13. Hint: Do not attempt to "compute" A. Instead, think about how A2 is related to T.] (b) Using (a), determine whether T is one-to-one and /or onto. Justify your answers. a (c) Consider the case where v = and w = Determine T explicitly as a vector in Ro. Hence, determine A in this particular case. (d) Returning now to to the general case, let P = Span { v, w} be the plane in Ro spanned by v and w. Referring to P, give a one-sentence description of what T does geometrically. No justification is necessary. Hint: Use part (c) for inspiration. A correct description will allow you to immediately see why A2 = I3 is true.]